Not really. You just have to try different numbers.
As to patterns, the probability of finding a prime goes down for higher numbers. The number of prime numbers up to a number "n" is roughly equal to n / ln(n), where ln() is the natural logarithm function.
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Nobody. That is because there is no pattern to prime numbers. There are various methods to find some classes of prime numbers but none that will find all of them.
No one has ever discovered the mathematical pattern for prime numbers and all that is known about them is that each prime number has only 2 factors which are itself and one.
by finding the prime numbers up to 100
In part because the problem of finding large prime numbers isn't exactly trivial.
1 Prime numbers have only 2 factors which are themselves and one 2 Prime numbers can't be composite numbers which have more than 2 factors 3 Prime numbers are odd except for two which is the only even prime number 4 Prime numbers are used in finding the LCM of 2 or more numbers 5 Prime numbers are used in finding the HCF of 2 or more numbers 6 Prime numbers are used in finding the LCD of fractions 7 Prime numbers are used in reducing fraction to their lowest terms 8 Prime numbers are rational because they can be expressed as fractions 9 Prime numbers are infinite 10 Prime numbers are irrational when square rooted 11 Prime numbers can't be 0 or 1 which are also not composite numbers 12 Prime numbers don't follow a forecasted numerical pattern 13 Prime numbers make up 25% of the first 100 integers or whole numbers 14 Prime numbers have a code amongst themselves that has never been cracked